I'm having a problem in that the position of an exponent, relative to the base, is too low. For example, with capital letters or mathbb the top of the exponent is almost in line with the top of the base. With mathbb the exponent is slightly lower (!) than the base. That is,
\mathbb{R}^n produces a result such that the top of the "n" is a little lower than the top of the "R". The size is correct, but the alignment is just off. It looks OK when small characters are exponentiated. I'm sure there's a setting somewhere I'm just missing, but I'm not using any exotic packages or configurations. What can I do to fix this?

This is a picture of what the example provided by Mico looks like on my system.

Update: Something in with the AMS book document class was causing this. Once I changed the document class to the standard {book} that problem (and many other annoying conventions) went away.

For your example I get an exponent that is perfectly in line with the top of the line of text. I think this is the normal behavior for inline math (i.e. between $ or \(..\)): TeX tries to keep the mathematics in the same line as the surrounding text. In displaystyle math (e.g. between \[...\]) the exponents are slightly higher.
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CaramdirNov 14 '11 at 23:42

1 Answer
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When a formula with base and exponent is being typeset in "textstyle" mode, TeX sets the base in textstyle size and the exponent in "cramped scriptsize". On the other hand, when the same formula is typeset in "displaystyle" mode, TeX sets the base in textstyle but the exponent in "non-cramped scriptsize". The "cramped" vs "non-cramped" mode doesn't affect the size of the exponents (they're both in "scriptsize") but, rather, their vertical placement. As the name suggests, "cramped" means in the present case that a superscript isn't raised as much as it is in non-cramped mode. See chapter 17 of the TeXbook for an exhaustive listing of the ways in which decides to be in cramped vs non-cramped mode.

The following MWE illustrates the effects of being in textstyle math vs is displaystyle math for the relative positioning of the exponents: the first two expressions are typeset in textstyle, the next two are in displaystyle.

Unfortunately, the displaystyle command doesn't alter significantly the alignment of the exponent, e.g., $\displaystyle R^n$ It still displays in-line with base; it looks nothing like your example.
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3SphereNov 15 '11 at 3:05

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Please provide a MWE that illustrates what's going on, with information on the version of TeX you're using.
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MicoNov 15 '11 at 3:28

I'm not sure what you mean by "MWE"; I'm using the latest version of MiKTex + PDFLatex.
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3SphereNov 15 '11 at 12:42

Sorry for the jargon: MWE is short for "Minimum Working Example," which should be (i) a standalone latex program that reproduces the problems you're experiencing and (ii) is "minimal" in the sense that it doesn't contain material not pertinent to the issue at hand. I.e., don't post your entire thesis...
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MicoNov 15 '11 at 13:44

I entered the example exactly as you supplied it into a new document.
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3SphereNov 15 '11 at 15:12